Type: Seminar

Modified: Wed 24 Aug 2011 0746

Distribution: World

Expiry: 26 Aug 2011

Auth: carberry@14-200-76-88.static.tpgi.com.au (carberry) in SMS-WASM

Next Friday 26 August we have a fabulous double-header of talks with Marston Conder (University of Auckland) giving a colloquium at 12 PM (the usual algebra seminar slot) on Symmetry and Chirality in Discrete Structures and Peter Sarnak (Princeton University/IAS) presenting his Mahler lecture at 2:30 PM on Zeroes and Nodal Lines of Modular Forms. All are welcome to join for the lunch in between these talks at 1 PM at the Forum restaurant. On Thursday 25 August Peter Sarnak will give a public lecture at the University of New South Wales, 3:30 PM on Chaos, Quantum Mechanics and Number Theory. Information on the Mahler Lectures and details of the three talks are below. ------------------------------------------------------- The Mahler Lectures are a biennial activity organised by the Australian Mathematical Society with the assistance of the Australian Mathematical Sciences Institute. Initiated by a bequest from number theorist Kurt Mahler, it brings a renowned mathematician to Australia to give a lecture tour (including public lectures) of Australian universities. This year’s Mahler lecturer is Peter Sarnak, Eugene Higgins Professor of Mathematics at Princeton University and Professor at the the Institute for Advanced Study in Princeton. He is a legendary figure in modern number theory. Peter Sarnak will be in Australia from August 8 till August 27 and will give 13 lectures at 9 different universities in 6 different cities. ----------------------------------------------------------------- Speaker: Marston Conder, University of Auckland Date: Friday 26 August, 12:05-12:55pm Location: Carslaw 175 Title: Symmetry and chirality in discrete structures Abstract: Symmetry is pervasive in both nature and human culture. The notion of chirality (or ‘handedness’) is similarly pervasive, but less well understood. In this lecture I will talk about a number of situations involving discrete objects that have maximum possible symmetry in their class, or maximum possible rotational symmetry while being chiral. Examples include graphs (networks), maps (graphs embedded on surfaces), compact Riemann surfaces (equivalence to algebraic curves), and polytopes (abstract geometric structures). In such cases, maximum symmetry can often be modelled by the action of some universal group, the non-degenerate quotients of which are the symmetry groups of individual examples. The use of computational systems (like MAGMA) can be very helpful in producing examples, and then revealing patterns among them, or providing answers to various questions. An intriguing question in some of these situations is about the prevalence of chirality: among small examples, how many are reflexible and how many are chiral? and what happens asymptotically? ........................................................................... 1 PM: Lunch at the Forum Restaurant, Darlington Centre. All welcome. ------------------------------------------------------- Friday, Aug. 26, Sydney University, 2.30pm, Room 175, Carslaw Building, Colloquium Zeroes and Nodal Lines of Modular Forms One of the consequences of the recent proof by Holowinski and Soundararajan of the holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of a classical holomorphic hecke cusp forms become equidistributed as the weight of the form goes to infinity. We review this as well as some finer features (first discovered numerically) concerning the locations of the zeros as well as of the nodal lines of the analogous Maass forms. The latter behave like ovals of random real projective plane curves, a topic of independent interest. -------------------------------------------------------